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=(1)/(2) 4. If (x-1)/(y+3)-(x)/(y)=(1)/(z), find x when y=8 and z=2.

=12 =\frac{1}{2} \newline44. If x−1y+3−xy=1z \frac{x-1}{y+3}-\frac{x}{y}=\frac{1}{z} , find x x when y=8 y=8 and z=2 z=2 .

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Find limits involving absolute value functionsright chevron icon

Full solution

Q. =12 =\frac{1}{2} \newline44. If x−1y+3−xy=1z \frac{x-1}{y+3}-\frac{x}{y}=\frac{1}{z} , find x x when y=8 y=8 and z=2 z=2 .
  1. Plug in values: Plug in the given values for yy and zz into the equation.x−18+3−x8=12\frac{x-1}{8+3}-\frac{x}{8}=\frac{1}{2}
  2. Simplify equation: Simplify the equation. x−111−x8=12\frac{x-1}{11}-\frac{x}{8}=\frac{1}{2}
  3. Find common denominator: Find a common denominator for the fractions on the left side of the equation, which is 8888. \newline8(x−1)88−11x88=12\frac{8(x-1)}{88}-\frac{11x}{88}=\frac{1}{2}
  4. Distribute and combine: Distribute and combine like terms. (8x−8−11x)/88=12(8x-8-11x)/88=\frac{1}{2}
  5. Simplify numerator: Simplify the numerator.−3x−888=12\frac{-3x-8}{88}=\frac{1}{2}
  6. Cross-multiply: Cross-multiply to get rid of the fractions.\newline−3x−8=44-3x-8=44
  7. Add 88 to both sides: Add 88 to both sides of the equation.\newline−3x=52-3x=52
  8. Divide to solve for xx: Divide both sides by −3-3 to solve for xx.x=−523x=\frac{-52}{3}

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